As depicted in Fig. REF , the following diagrams are included in constructing the reaction amplitudes: the \(s\) -channel nucleon and nucleon resonance exchanges, the \(t\) -channel \(K\)  and \(K^\ast \)  exchanges, and the interaction current. Note that the \(u\) -channel \(\Lambda \)  exchange is not considered as no information on the radial decay \(\Lambda (1690) \rightarrow \Lambda \gamma \)  is available in RPP [1]}. The full amputated reaction amplitude for the \(\gamma p \rightarrow K^+\Lambda (1690)\)  reaction can be expressed as
\(M^{\nu \mu } \equiv M^{\nu \mu }_s + M^{\nu \mu }_t + M^{\nu \mu }_{\rm int}, \) 
